Photoelectric Effect and Acceleration My question relates to the photoelectric effect. Namely: why is a photon not produced by the photoelectric effect? If an electron gains a certain amount of kinetic energy from the incident photon, do we not call this change in kinetic energy 'acceleration'? If so, I thought that all accelerating charges produce an EM wave (a photon?).
Is my assumption here that the electron accelerates, wrong? If so, why is it wrong?
Many thanks,
Steven
 A: It is not useful to think about it in terms of acceleration, because you don't know how it accelerates, you don't know if it has had a weak acceleration for longer time, or a strong acceleration for a shorter time. Fortunately, that's quite irrelevant...
You should think if more like a collision. Wen you study the impact of two billiard balls, you don't study acceleration; rather, you want to know the final direction and velocity of each ball...
A: Imagine an electron at rest, i.e. with zero kinetic energy. This electron is then accelerated and then stopped again. Both, the acceleration and the deceleration, would cause the emission of a photon according to your assumption. So this procedure would create two photons just like that. The electron has the same energy as initially. Therefore it would violate energy conservation.
Reality is different: An electron is accelerated not only by photon emission, but also by photon absorption. Which of these happens is given by energy conservation. This is why people usually describe the photoelectric effect as a collision, in which you care about the initial and final state, but not at the short interval of interaction.
A: All interactions of photons with quantum mechanically bound systems,atoms, molecules, lattices, mean that the photon is absorbed by the atom, molecule, lattice, the  electron finding itself in a higher energy level of the bound system, and the photon absorbed, except iff the photon has enough energy to ionize the atom, i.e. free an electron. The photoelectric effect. Note that the y axis says "maxmum kinetic energy" , as part of the energy of individual photon-lattice interactions could as a low energy photon,or lattice vibrations.
It is true that free accelerated electrons in a magnetic field for example, radiate . But the electron in the lattice is not free, it acquires  kinetic energy at ionisation once off, when  the photon is absorbed. Before that it is in an orbital, not an orbit, which has only a probability distribution for its position.
